Optimum Power Control for CDMA With Deterministic Sequences in Fading Channels

Abstract

Abstract-We specify the capacity region for a power-controlled, fading code-division multiple-access (CDMA) channel. We investigate the properties of the optimum power allocation policy that maximizes the information-theoretic ergodic sum capacity of a CDMA system where the users are assigned arbitrary signature sequences in a frequency flat-fading environment. We provide an iterative waterfilling algorithm to obtain the powers of all users at all channel fade levels, and prove its convergence. Under certain mild conditions on the signature sequences, the optimum power allocation dictates that more than one user transmit simultaneously in some nonzero probability region of the space of all channel states. We identify these conditions, and provide an upper bound on the maximum number of users that can transmit simultaneously at any given time. Using these properties of the sum capacity maximizing power control policy, we also show that the capacity region of the fading CDMA channel is not in general strictly convex.Index Terms-Capacity region, code-division multiple access (CDMA), fading channels, iterative waterfilling, power control, sum capacity.

Jointly optimal power and signature sequence allocation for fading CDMA

“…For any fixed channel state, the optimal choice of signature sequences for a given power control policy p(h) is an orthogonal set [5], [6]. Noting that the received power levels are p i (h)h i , solving (5) is equivalent to solving K independent Goldsmith-Varaiya problems [2] (see also [1]), the solution to which is a single user waterfilling for each user. The optimal solution p * (h) is the unique solution satisfying the Karush-Kuhn-Tucker (KKT) conditions, and is given by,…”

“…In the fading case with channel adaptive powers, as suggested by the results in [1]- [3], it is likely that some users will have powers equal to zero at some channel states, and they will not contribute to C sum at those channel states. Although the concept of oversized users is defined for users with nonzero average power constraints, since users which are allocated zero power at state h will not contribute to the sum capacity, we can add them to the set of non-oversized users at channel state h,L(h), and we can assume that we assign arbitrary sequences for those users without changing the solution.…”

“…To maximize the overall network capacity, one should therefore exploit the variations in the channel fade levels while allocating the available resources. Resource allocation for wireless systems can be viewed in several different contexts, including SIR-based approaches and information theoretic approaches (see [1] for some references on both). We can also group the allocation schemes according to the type of resources that are allocated.…”

“…Two important resources are the transmit powers and the transmit waveforms. Power control has been studied in SIR-based and information theoretic contexts for fading and non-fading channels [1]- [4], whereas waveform optimization has been studied in these two contexts for nonfading channels only [5]- [7]. Throughout this paper the objective of resource allocation is to maximize the information theoretic ergodic (expected) sum capacity, and we consider allocating both powers and the waveforms as functions of the channel state information (CSI) in order to achieve this objective.…”

“…The more generalized version of the power control problem with arbitrary signature sequences and arbitrary number of users and processing gain is solved in [1], where the solution is shown to be a simultaneous waterfilling of powers of users, and an iterative algorithm which performs a one-user-at-a-time single user waterfilling for each user, while the powers of all other users are fixed, is shown to converge to the optimal solution. The optimum power allocation in that case is shown to dictate more than one user to transmit simultaneously in certain regions of the channel state space, provided that the signature sequences satisfy some mild conditions.…”